X-Ray Crystallography The most important technique for mineralogy The most important technique for mineralogy Direct measurement of atomic arrangement Direct measurement of atomic arrangement Direct measurement of what was originally deduced from crystal faces Direct measurement of what was originally deduced from crystal faces

X-Rays Electromagnetic radiation – similar to visible light Electromagnetic radiation – similar to visible light = 0.02 to 100 Å = 0.02 to 100 Å = to 10 nm = to 10 nm Visible light = 400 to 750 nm Visible light = 400 to 750 nm

Fig. 6-6 Visible light spectrum Full range of electromagnetic radiation (nm) f (hertz) 1 nm = m } X-Rays

X-Ray generation  Heat filament, which discharges electrons  Electron accelerated with 20 to 100 kV toward “target”  Target is Cu or Mo (also Co, Fe and Cr) Very hot – requires continuous circulation of cooling water Fig. 8-2 Full spectrum of X rays

X-Ray generated  Continuous spectrum of X-ray energy (wavelengths) are produced without electrons changing shells  Characteristic spectrum when incoming electrons dislodge electrons from outer shells  Electrons drop from either M shell (K  ) or L shell (K  ) K  the most intense (highest energy) X-rays Target material - Cu Electrons KK KK Fig. 8-3

Use of X-rays requires single wavelength Use of X-rays requires single wavelength Similar to monochromatic visible light Similar to monochromatic visible light Wavelength critical for measurement Wavelength critical for measurement Acts like a “ruler” Acts like a “ruler” Must filter out the continuous spectrum, and leave only one of the characteristic spectrum Must filter out the continuous spectrum, and leave only one of the characteristic spectrum Typically K  peak – most intense Typically K  peak – most intense Referred to as Cu – K  radiation Referred to as Cu – K  radiation

Filtering Use a monochrometer Use a monochrometer Typically a thin piece of Ni or Be foil Typically a thin piece of Ni or Be foil Foil allows most Cu-K  radiation to pass Foil allows most Cu-K  radiation to pass Blocks most wavelengths except K  Blocks most wavelengths except K  Absorption edge, Ni filters out these wavelengths X-rays pass through filter X-rays blocked by filter = Å = Å

Detection Variety of detectors Variety of detectors Scintillation counters (light flashes) Scintillation counters (light flashes) Gas proportional counters Gas proportional counters Detectors are arranged so that X-rays reflected off of mineral surfaces can be recorded Detectors are arranged so that X-rays reflected off of mineral surfaces can be recorded Detector Sample Arrangement of X-Ray diffractometer X-ray generation

X-Ray diffraction Wavelength of X rays 1 to 2 Å Wavelength of X rays 1 to 2 Å Cu K  = Å Cu K  = Å About the same length as spacing of atoms in minerals About the same length as spacing of atoms in minerals Typically 1 to 2 Å Called d spacing = Å

X-Ray diffraction pqr = n pqr = n pq = d sin  Reflects waves in phase, only if angle  is such at that the additional distance pqr traveled by wave 2 is an integer number of wavelengths (here 1 wavelength)

Bragg Equation pqr = n pqr = n pq = d sin  pqr = 2pq = 2d sin  = n 2d sin  = n Bragg Equation Planes of atoms

Example Halite – {111} planes have d spacing of Å Halite – {111} planes have d spacing of Å Cu K  radiation, = Å Cu K  radiation, = Å Solving Bragg equation shows Solving Bragg equation shows  = 13.70º for n = 1  = 13.70º for n = 1  = 28.27º for n = 2  = 28.27º for n = 2  = 45.27º for n = 3  = 45.27º for n = 3  = 71.30º for n = 4  = 71.30º for n = 4 When X-rays reflect off mineral at these angles, they will interfere constructively – cause a peak in energy at the detector

Multiple possible atomic planes {110}, {100}, {001} etc. Multiple possible atomic planes {110}, {100}, {001} etc. Orienting a single grain unlikely to reflect X-rays off of any of these planes Orienting a single grain unlikely to reflect X-rays off of any of these planes Better to use multiple grains with random orientations Better to use multiple grains with random orientations With enough planes (1000’s), there will be enough parallel to create reflections. With enough planes (1000’s), there will be enough parallel to create reflections. Powder Diffraction method Powder Diffraction method

Powder Diffraction Sample crushed to small size, typically < 0.05 mm Sample crushed to small size, typically < 0.05 mm Placed on glass slide or hollow holder Placed on glass slide or hollow holder Sample placed in X-Ray diffractometer Sample placed in X-Ray diffractometer Blasted with X-rays as sample and detector rotate from around 2º to 70º Blasted with X-rays as sample and detector rotate from around 2º to 70º

Degrees 2  Intensity of reflection Strip recorder records intensity of signal from detector

Data reduction Powder diffraction files Powder diffraction files Cards with the intensity and d spacing for all minerals Cards with the intensity and d spacing for all minerals 4 major peaks, d spacing All peaks, d spacings relative intensity, reflecting plane

Take rock, sediment, mineral sample Take rock, sediment, mineral sample Grind sample Grind sample Mount Mount Measure all d spacings Measure all d spacings Compare with the powder diffraction files Compare with the powder diffraction files